Advances in Condensed Matter Physics

Volume 2019, Article ID 4256526, 7 pages

https://doi.org/10.1155/2019/4256526

## Thickness Induced Line-Defect Reconfigurations in Thin Nematic Cell

^{1}Faculty of Mathematics and Natural Sciences, University of Maribor, Koroška 160, Maribor, Slovenia^{2}Jožef Stefan Institute, Jamova 39, Ljubljana, Slovenia^{3}Faculty of Industrial Engineering, Šegova 112, Novo mesto, Slovenia

Correspondence should be addressed to M. Ambrožič; is.mu@cizorbma.nalim

Received 29 November 2018; Accepted 10 February 2019; Published 4 March 2019

Guest Editor: Jiajie Zhu

Copyright © 2019 M. Ambrožič and S. Kralj. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We studied the impact of the cell thickness on configurations of line disclinations within a plane-parallel nematic cell. The Lebwohl-Lasher semimicroscopic approach was used and (meta)stable nematic configurations were calculated using Brownian molecular dynamics. Defect patterns were enforced topologically via boundary conditions. We imposed periodic circular nematic surface fields at each confining surface. The resulting structures exhibit line defects which either connect the facing plates or remain confined within the layers near confining plates. The first structure is stable in relatively thin cells and the latter one in thick cells. We focused on structures at the threshold regime where both structures compete. We demonstrated that “history” of samples could have strong impact on resulting nematic configurations.

#### 1. Introduction

Line topological defects are ubiquitous in nematic liquid crystals (NLC) which is fingerprinted even in their name [1]. They could be stabilised topologically by appropriate boundary conditions [2, 3] or due to energy reasons [4]. They have a strong impact on optical NLC properties and are therefore of potential interest for various electro-optic applications.

Nematic uniaxial liquid crystals exhibit simultaneously liquid properties and local orientational order [5]. The latter is at macroscopic level commonly presented by the nematic director field . It points along the local uniaxial order, where states with are physically equivalent. In bulk equilibrium is spatially homogeneous and aligned along a single symmetry breaking direction. NLC can exhibit line dislocations, which are characterised by the winding number* m* = ±1/2 [6, 7]. It reveals the total reorientation of on encircling the defect in counter-clockwise direction. Furthermore, one can assign the total topological charge* q* to a line defect [6] by enclosing it by a surface. This charge is integer and reveals how many realizations of all orientations are realised in the nematic order parameter space [6]. Note that the core structure of line* m* = ±1/2 line defects is biaxial [8], and the center of the core exhibits negative uniaxiality.

Line defects could be stabilised in different ways. For example, they could be enforced by AFM imprinted patterns to plates enclosing NLC in plane-parallel geometry as illustrated in [2]. It has been shown [9] that, in such geometries the line defects could either span the opposite plates or are confined to the vicinity of the bounding plates. In this paper we focus on these competing structures. We henceforth refer to the defect configurations that (i) connect the bounding plates and (ii) remain confined close to the planes, as the (i)* connected* and (ii)* confined *defect configurations, respectively. In our study we consider networks of line defects in a plane-parallel cell of thickness* h*. We use the Lebwohl-Lasher semimicroscopic lattice model [10, 11] where the local orientational order is presented by nematic pseudospins. We assume that the bounding plates are patterned by a lattice of concentric circles, enforcing the circular planar nematic alignment, which give rise to line defects. We focus on the impact of* h* and history of samples on defect patterns. The plan of the paper is as follows. In Section 2 we present model and in Section 3 results. In the final section we summarize our results.

#### 2. Materials and Methods

We consider nematic structures within a plane-parallel cell of thickness* h*. At the bounding plates we enforce spatially varying nematic patterns and calculate the corresponding nematic structures within the cell. In our modelling we use the semimicroscopic Lebwohl-Lasher lattice approach [10, 11]. In this modelling the nematic orientational ordering is described in terms of nematic spins (states with are physically equivalent) residing at each lattice site. We henceforth refer to unit vectors as* spins*. The simulation lattice is cubic, characterised by the lattice constant* a*_{0}.

The simulation lattice consists of* M* ×* M* ×* L* sites in the Cartesian coordinate system (*x*,* y*,* z*). Here* L* is proportional to the cell thickness, i.e.,* h* =* La*_{0}, while* M ** L* stands for its lateral dimensions. In the following we set* a*_{0} = 1, so that we identify* L* with the cell thickness. Individual sites are denoted by a set of indices (*i*,* j*,* k*): 1 * i* ≤* M*, 1 * j* ≤* N*, and 1 * k ** L*. Each site is occupied by a* spin *, which tends to orient in parallel direction with its nearest neighbors. The bounding plates have imprinted a two-dimensional (2D) circular nematic “surface field” (see Figures 1 and 2, top left), which enforces line defects to the LC body. Therefore, we impose a lattice of two-dimensional* m * 1 topological point defects. This surface imprinted structure is positioned symmetrically on both plates. In the model the surface field is determined by frozen-in* spins* at the bounding plates.